Pauli channel tomography with unknown channel directions

TL;DR

This paper presents a method for estimating the parameters and directions of a qubit Pauli channel simultaneously using channel matrix formalism, highlighting optimal strategies for different parameter estimations.

Contribution

It introduces a novel approach that does not assume known channel directions, enabling joint estimation of channel parameters and directions in quantum tomography.

Findings

Optimal input states and measurements for contraction parameter estimation

Different tomography conditions improve channel direction estimation

Method enhances accuracy of quantum channel characterization

Abstract

In this paper we estimate the parameters of the qubit Pauli channel using the channel matrix formalism. The main novelty of this work is that we do not assume the directions of the Pauli channel to be known, but they are determined through the tomography process, too. The results show that for optimally estimating the contraction parameters and the channel matrix we should have input qubits and measurements in the channel directions. However, for optimally estimating the channel directions, we should use different tomography conditions.